(i) Let $D \subset \mathbb{C}$ be a domain, let $f: D \rightarrow \mathbb{C}$ be an analytic function and let $z_{0} \in D$. What does Taylor's theorem say about $z_{0}, f$ and $D$ ?

(ii) Let $K$ be the square consisting of all complex numbers $z$ such that

$$-1 \leqslant \operatorname{Re}(z) \leqslant 1 \text { and }-1 \leqslant \operatorname{Im}(z) \leqslant 1,$$

and let $w$ be a complex number not belonging to $K$. Prove that the function $f(z)=$ $(z-w)^{-1}$ can be uniformly approximated on $K$ by polynomials.